Open AccessProximity Between Selfadjoint Operators and Between Their Associated Random Measures
Author(s) -
Alain Boudou,
Sylvie Viguier-Pla
Publication year - 2018
Publication title -
european journal of pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.245
H-Index - 5
ISSN - 1307-5543
DOI - 10.29020/nybg.ejpam.v11i4.2552
Subject(s) - mathematics , bounded function , commutative property , set (abstract data type) , operator theory , pure mathematics , order (exchange) , relation (database) , spectrum (functional analysis) , mathematical analysis , discrete mathematics , data mining , physics , finance , quantum mechanics , computer science , economics , programming language
We study how the proximity between twoselfadjoint bounded operators, measured by a classical distance, canbe expressed by a proximity between the associated spectralmeasures. This last proximity is based on a partial order relation on the set of projectors. Assuming an hypothesis of commutativity, we show that the proximity between operators implies the one between theassociated spectral measures, and conversally, the proximity between spectral measures implies the one between associated selfadjoint operators.